More Unit #3 Review Questions

SPH 3U

More Unit #3 Review Questions

1. State the reaction force for each of the following forces.

(a) the southward force of a field goal kicker’s toe on a football

(b) the backward force of a jogger’s shoe on the ground

(d) the backward force of a jet’s engines on its exhaust gases

(e) the backward pull of a swimmer’s hands on the water in the butterfly stroke

2. A beginning physics student, confused by a seeming contradiction in Newton’s laws, asks her teacher the following question: “If, for every force there is an equal and opposite reaction force, then all forces in nature come in equal and opposite pairs, and are therefore balanced. Thus, since there can never be such a thing as an unbalanced force, how can any object ever accelerate?” Explain the fault in this common misconception.

3. A squirrel with an armful of nuts is sliding helplessly across the flat, icy roof, getting dangerously close to the edge. He understands Newton’s Third Law, and is able to save himself. Explain how he does it.

4. Two crates, of mass 12.0 kg and 20.0 kg, respectively, are pushed across a smooth floor together, the 20 kg crate in front of the 12 kg crate. Their acceleration is 1.75 m/s2. Calculate each of the following.

(a) the force applied to push the crates

(b) the action-reaction forces between the two crates

Recalculate (a) and (b) if the relative positions of the two crates are reversed.

5. A locomotive with a mass of 2.0 ´ 104 kg accelerates from rest to a velocity of 2.0 m/s in 5.0s. If it is pulling a train of 20 cars, each of mass 1.0 ´ 104 kg, what is the force in the coupling at each of the following points?

(a) between the locomotive and the first car

(b) between the 10th car and the 11th car

6. Three small children of mass 20.0 kg, 24.0 kg, and 16.0 kg, respectively, hold hands, as shown, and are pulled across a smooth frozen pond by a larger boy on skates, who pulls a horizontal rope being held by the first child. The skater pulls on the rope with a force of 135 N. Calculate each of the following.

(a) the acceleration of the skater

(b) the force with which each pair of children must hold hands, to ensure that the chain is not broken

7. A 0.50 kg skateboard is at rest on a rough, level floor on which two lines have been drawn 1.0 m apart. A constant horizontal force is applied to the skateboard at the beginning of the interval, and is removed at the end. The skateboard takes 8.5 s to travel the 1.0 m distance, and it then coasts for another 1.25 m before coming to rest. Calculate the force applied to the skateboard, and also the constant frictional force opposing its motion.

8. Two girls, one of mass 40 kg and the other of mass 60 kg, are standing side by side in the middle of a frozen pond. One pushes the other with a force of 360 N for 0.10 s. The ice is essentially frictionless.

(a) What is each girl’s acceleration?

(b) What velocity will each girl acquire in the 0.10 s that the force is acting?

9. A motorist has a reaction time of 0.60 s. (Reaction time is the interval between seeing a danger and applying the brakes.) While driving at 72 km/h, he sees a child run suddenly onto the road, 40 m in front of his car. If the mass of the car is 1000 kg and the average horizontal force supplied during braking is 8000 N, will he be able to stop in time to avoid hitting the child?

10. A child’s wagon experiences a frictional force of 73 N whenever it is in motion, regardless of the load it is carrying. An applied horizontal force of 128 N causes the wagon to accelerate at 5.0 m/s2. The same applied force, with a child on the wagon, causes it to accelerate at 1.0 m/s2. What is the mass of the child?

11. A net force of 8.0 N gives a mass m1 and acceleration of 2.0 m/s2 and a mass m2, an acceleration of 4.0 m/s2. What acceleration would the force give the two masses if they were fastened together?

More Unit #3 Review Questions – Solutions

1. (a) the northward force of the football on the kicker’s toe

(b) the forward force of the ground on the jogger’s shoe

(d) the forward force of the exhaust gases on a jet engine

(e) the forward force of the water on the swimmer’s hands

2. For forces to be “balanced,” they must act on the same object and be equal and opposite. The reaction to any force does not act on the same object as the force; it acts in the opposite direction on the agent exerting the original force. Thus, when considering the motion of one object, we look at the force, and when considering the motion of the agent of this force, we look at the reaction.

3. He saves himself by throwing nuts towards the edge of the roof. To do so, he exerts a force on each nut towards the edge. The nut exerts an equal force back on the squirrel, away from the edge, causing him to slow down.

(a)

(b) Consider the 20 kg crate only. The force accelerating it is the force exerted on it by the 12.0 kg crate, .

For the reversed crates, is unchanged but

(a) For the entire train,

For the force between the locomotive and the 1st car, the total mass being accelerated by this force is 20 cars of mass 1.0 ´ kg each.

(b) For the force between the 10th and 11th car,

For the acceleration of the entire group,

(b) For the force between the 20.0 kg and the 24.0 kg child, mass being accelerated is 16.0 kg + 24.0 kg.

Similarly, for the force between the 24.0 kg and 16.0 kg child,

Free body diagrams of the 3 children appear as:

For the first interval of motion, when Fa and Ff are acting:

For the second interval of motion, when only Ff is acting:

(a)

(b)

(c)

The car stopped 3.0 m short of hitting the child.

10.

Without the child,

With the child,

The mass of the child is 55 kg – 11 kg = 44 kg.

11.