1. A cart on a horizontal track is attached via a string and pulley to a hanging
ID: 1411947 • Letter: 1
Question
1. A cart on a horizontal track is attached via a string and pulley to a hanging weight.The weight of the hanging mass is .2 kg and the cart accelerates at 3.8 m/s2.What is the mass of the cart?
2. Another cart with a mass of .75 kg is on a horizontal track.One end of the cart is attached via string a pulley to a hanging weight with a mass of .3 kg, while the other end of the cart is attached similarly to a weight of mass .5 kg.In this problem, the positive direction is the direction toward the .3 kg mass.What is the acceleration of the cart?
3. A block of wood with a mass of .25 kg experiences a force just strong enough to start the block moving (friction is a factor in this case).The force that caused the block to begin moving remains constant, even after the block begins to slide.If the coefficient of static friction s is .4 and the coefficient of kinetic friction k is .15, what is the acceleration of the block after it begins to move?
4. A centripetal force is a force that pulls an object into a circular motion.If you attach a ball to a string and twirl it around your finger you are using the string to exert a centripetal force on the ball.If you are driving around a tight turn in your car, centripetal force due to tire friction is what makes the car turn instead of sliding off the road.The equation for a centripetal force is
F = mv^2/r
You are driving down a windy country road and come to a particularly tight curve. The mass of your car is 1500 kg, and the coefficient of static friction s between tires and dry pavement is .7; the radius of the road curve is 80 m and you are traveling at 25 m/s (around 55 mph). If you take the curve at this speed, will the friction from the tires be able to hold you on the road, or will you slide off the edge into the ditch? First, find the force due to friction, and then compare it with the centripetal force needed to keep the car on the road; then use that comparison to answer the question. (This problem, by the way, is the reason that a lot of curves on highways are slightly banked; that is, they angle the surface of the roadway so that it tips slightly toward the center of the road curve. This helps the tire friction to keep the car on the road.)
5. A rabbit is being chased by wolves in the winter.The rabbit thinks that a good way to escape the wolves is to jump and slide across a nearby frozen river that is 60 m wide; however, if it can’t make it all the way across, it will be trapped since the ice is too slippery for the rabbit to run on.In such a case, the only force acting upon the rabbit will be friction.The mass of the rabbit is 1.7 kg, and the coefficient of kinetic friction k for ice is .15. If the rabbit is initially running at 18.6 m/s, how far could the rabbit slide from the edge of the river before it stops? Will the rabbit make it across? (Hint: this is a two step problem. First, use Newton’s second law to find the rabbit’s acceleration; then use the kinematic relationship: to find the distance traveled.)
Explanation / Answer
equation of motion of the hanging mass
mg - T = ma
0.2 * 9.8 - T = 0.2 * 3.8
T = 1.2 N
equation of motion of block
T = ma
1.2 = m * 3.8
m = 0.315 kg
mass of the block = 0.315 kg
2)
equation of motion of the block
-0.5 * 9.8 + 0.3 * 9.8 = 0.75 * a
a = -2.613 m/s^2
acceleration of the block = -2.613 m/s^2
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