1A Week 3 Tutorial Questions Fall 1998

Physics 1AWeek 3 QuestionsFall 1998

1. A boy and a girl stand on a frictionless patch of ice a distance of 20 m apart, holding a taut rope between them. The girl is the heavier of the two.

a) When they pull on the rope, they both move. Explain.

b) Will they meet at a point closer to the girl's original position, or the boy's original position? Explain.

c) Let the girl's force be 50N, and the masses be 40 kg for the boy and 60 kg for the girl. Calculate the position where they meet. Does your calculation agree with your answer to part (b)?

2. Take your bathroom scales to an elevator in a tall building, put them down and stand on them, start at the ground floor. When the elevator is at rest, the scales read the same as they would in your bathroom. Press the button for the 20th floor. What will the scales read as the elevator starts to go up? What will they read as the elevator slows down to a stop at the 20th floor? What will they read for most of the journey between, say, the 3rd and the 17th floors? What will they read as you start your journey down? What would they read if the elevator cable broke?

3. What does a spring scale read in the following situations?

4. A 40N box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.20, and the coefficient of sliding friction is 0.10.

a) What is the frictional force exerted on the box if no other horizontal forces are present?

b) If a 4N force is exerted horizontally on the box, what will the frictional force be?

c) What is the minimum force needed to move the box?

d) What is the minimum force required to keep the box in motion once it has started?

e) If the horizontal force is 12N, how great is the frictional force?

5. NASA has a great big centrifuge that they use to test how large a 'g' force human beings can tolerate before they black out. (This is important information to know for high speed flight). The machine has an arm of length 15m that whirls around a circular track at 1 rev per 4 seconds. The test subject (mass 70 kg) sits strapped in a chair at the end of the arm and must keep a button pressed to keep the machine turning. What acceleration does the victim feel? What force is exerted on the victim by the chair?

Physics 1AWeek 3 SolutionsFall 1998

1. Boy pulls on girl with force T, girl pulls on boy with force T, both move, boy moves most (lower mass), so they meet nearer girl's original position. Boy's acceleration is 3/2 times girl's, distance traveled in time t is proportional to acceleration (initial velocity = 0), so boy moves 3/2 times distance girl moves, boy must move 12m and girl 8m.

2. The upward force on you from the floor, or the scales, is what you perceive as your weight. It is really the normal force. If this force equals your weight, you are in equilibrium (as you usually should be in your bathroom). If you are accelerating upwards (e.g. the beginning of a ride up in the elevator, or the end of a ride down), the net vertical force on you must be upwards, i.e. the normal force is larger then your weight. You have the sensation of being heavier than usual, and the scale reads a larger number. When you are accelerating downwards the scales will read a lower value. When you are travelling at constant speed the scales will read the usual number.

3. A spring scale reads:

4.a) You have a box on a rough horizontal surface. You are not pushing on it. Forces of gravity and the normal force are equal and opposite, hence balance each other. Does the box move? No. Box is in equilibrium, so friction force is zero. Remember for static friction. This allows the friction force to be as small as zero and as large as .

b) The normal force FN = 40N, ms = 0.20, so the max. possible value of the force of static friction is = 0.2 x 40N = 8N. So a 4N push on the box will not be able to move the box. So the friction force will balance the push force (i.e. Ff = 4N).

c) As calculated in part (b) the max value of the static friction force is 8N. So we will need a force just a bit larger than 8N to make it move.

d) If the box is to keep moving at constant speed we have to apply a force to balance the force of kinetic friction. Ff = mk FN = 0.1 x 40N = 4N is the force of kinetic friction. So we must push with a force of 4N.

e) 12N is greater than the max static friction force, so the box will move. If the box is moving the kinetic friction force is 4N, regardless of how fast it is going. So the friction force is due tokinetic and is 4N. The box will now have a net horizontal force of (12N - 4N) = 8N and will accelerate.

5. The acceleration towards the center of the circle is a = v2/R, where v = 2pR/t and t = time. To complete one circle, t = 4 sec, hence v = 23.6 m/s and a = 37.0 m/s2. The force towards the center of the circle is F = mv2/R, giving F = (70 kg) x 37 m/s2 = 2590N. The chair also has to support the future astronaut against the force of gravity, so there must be an upwards force of (70 kg) x 10 m/s2 = 700N. The total force will be the sum of the 2590N horizontal force and the 700N vertical force.