3.1 Forces

A yoga practitioner with a weight of 686 N is standing motionless on a horizontal floor with both feet on the ground.  He changes to a new pose where one leg is lifted in the air, so that he is now standing motionless with only one foot on the ground.

State, with a reason, what the difference is between the total normal reaction force exerted by the floor on the yoga practitioner when he has both feet on the ground, and the total normal reaction force when he has only one foot on the ground.

Given that the particle in each of the following diagrams is in equilibrium, work out the value of :

The following force diagram depicts a particle moving with constant velocity, :

Determine the values of  and .

A pallet of large cheeses is being lowered into a cave for storage. The total weight of the pallet and cheeses is 17000 N, and to make sure that the pallet remains level while it is being lowered, the same tension, , is maintained in each of the two support ropes. Other than the weight of the pallet and cheeses, and the tension in the ropes, all other influences on the motion of the pallet can be ignored.

Given that the pallet is moving vertically downwards at a constant speed, work out the tension, , in each rope.

The tension in each rope is now increased by 500 N.

Describe the resulting motion of the pallet immediately following the change in tension, being sure to explain the physical reasoning behind your answer.

A train locomotive is moving along a horizontal level track. The locomotive’s engine provides a forward thrust of 75 000 N. The total resistance is modelled by a constant force of  N. The locomotive is not pulling any other train cars.

Modelling the locomotive as a particle, draw a force diagram to show the forces acting on the locomotive.

Given that the resultant force acting on the locomotive is 71 800 N in the direction of the locomotive’s motion, find the value of .

A particle is acted upon by two forces,  and , given in vector form as

where  is a constant.

Find the angle between  and .

The resultant of  and  is .

Given that  is parallel to the vector , find the value of .

A particle is acted upon by three forces,  given in vector form as

where  and  are constants.

Given that the particle is in equilibrium,

Find the values of the constants  and .

The magnitude of force  is now halved, while its direction remains the same. The resultant of the three forces after this change is .

Find the magnitude of  and the angle that it makes with the vector .

As part of an acrobatics display, one acrobat with a weight of 735 N is standing motionless on a horizontal floor. Another acrobat with a weight of 495 N is standing motionless on the first acrobat’s shoulders. State, with a reason, what the total normal reaction force exerted by the floor on the first acrobat is, and in what direction it is acting.

Given that the particle in each of the following diagrams is stationary, work out the value of :

The following force diagram depicts a particle in equilibrium:

By setting up and solving a pair of simultaneous equations, find the values of  and .

On a building site, a pallet of large stone blocks is being raised by a crane. The total weight of the pallet and blocks is 22000 N, and to make sure that the pallet remains level while it is being raised, the same tension, , is maintained in each of the two lifting cables.  Other than the weight of the pallet and blocks, and the tension in the cables, all other influences on the motion of the pallet can be ignored.

Given that the pallet is moving vertically upwards at a constant speed, work out the tension, , in each cable.

The tension in each cable is now increased by 1000 N.

Describe the resulting motion of the pallet, being sure to explain the physical reasoning behind your answer.

A truck with a total weight of 27000 N is moving along a horizontal level road. The truck’s engine provides a forward thrust of 13500 N. The total resistance is modelled by a constant force of 1700 N. All other forces acting on the truck may be ignored.

Modelling the truck as a particle, draw a force diagram to show the forces acting on the truck.

Calculate the magnitude and direction of the resultant force acting on the truck.

A particle is acted upon by two forces,  given in vector form as

where  is a constant.

Find the angle between  and .

The resultant of  is .

Given that  is parallel to the vector , find the value of .

A particle is acted upon by three forces,  given in vector form as

where  are constants.

Given that the particle is in equilibrium,

Find the values of the constants .

The force  is now removed. The resultant of forces  is .

Find the magnitude of   and the angle that it makes with the horizontal.

A tourist with a weight of 1246 N is riding in a lift to the top of the Empire State Building in New York City. On his back he has a backpack full of  ‘I Love New York’ souvenirs, with a total weight of 352 N. The lift is moving vertically upwards at a constant speed of , and the tourist is standing still on the horizontal floor of the lift waiting for it to reach the top. 

State, with a reason, the magnitude and direction of the total normal reaction force exerted on the tourist by the floor of the lift.

Given that the particle in each of the following diagrams is moving with constant velocity, , work out the value of :

The following force diagram depicts a particle at equilibrium:

Given that  and , determine the values of .

In a slate quarry a load of slates is being raised to the surface for processing. The total weight of the slates and the platform on which they rest is 21000 N, and to make sure that the platform remains level while it is being raised, the same tension, T, is maintained in each of the two lifting cables. Other than the weight of the platform and slates, and the tension in the cables, all other influences on the motion of the platform can be ignored.

Given that the platform is moving vertically upwards at a constant speed of , work out the tension, ,  in each cable.

As it passes one of the levels in the quarry, two workers with a combined weight of 1600 N jump onto the centre of the slow-moving platform, hoping to catch a ride to the surface at the end of their shift.

Given that the tension in the cables stays the same, and that the platform remains perfectly level, describe the resulting motion of the platform after the workers jump onto it. Consider both the time immediately after they jump on as well as the longer term implications for the motion of the platform.  Be sure to explain the physical reasoning behind your answer.

A monorail train is moving along a horizontal level track. The train’s engine provides a forward thrust of  N.  The total resistance is modelled by a constant force of  N.

Modelling the train as a particle, draw a force diagram to show the forces acting on the train.

Given that

• the train’s speed is increasing in its direction of motion
• the resultant force acting on the train is 4200 N
• of  and , 9 times the magnitude of the smaller force is equal to 2 times the magnitude of the larger force

Find the values of  and .

A particle is acted upon by two forces,  and , given in vector form as

where  and  are constants with .

Find the angle between  and .

The resultant of  and  is .

Given that  is parallel to the vector , and that , find the values of .

A particle is acted upon by three forces,  given in vector form as

where  and  are constants.

Given that the particle is in equilibrium,

Find the values of the constants  and .

Force  is now removed, and another force  is applied in its place. The resultant of the three forces  is .

Given that is parallel to the vector , and that the angle between  and the vector  is ,  find the two possible values of the magnitude of . Your answer in each case should be given as an exact value.