1. A force of 150 N is continuously applied to an object with a mass of 11 kg over a distance of 2.5 m. The object slides over a surface with a coefficient of kinetic friction of .3. How fast is the object moving immediately after the force ceases to be applied?
2. A block of mass .4 kg is given an initial velocity of 4.2 m/s on a horizontal frictionless surface.
a. The block encounters a spring with a spring constant of 3000 N/m that is situated on a surface with a coefficient of kinetic friction of .4. How far will the block compress the spring?
(remember to account not only for energy stored in the spring but also energy lost; will need to use quadratic formula, or a solve function on your calculator)
b. After the block is stopped by the spring, the spring pushes the block in the other direction (remember that for the distance x that the spring was compressed, the block will be influenced by friction, but afterwards it will not). Eventually, the block passes the point at which it started and
c. b. After the block is stopped by the spring, the
d. spring pushes the block in the other direction (remember that for the distance x that the spring was compressed, the block will be influenced by friction, but afterwards it will not). Eventually, the block passes the point at which it started and slides up a ramp until it stops. How high (vertically) did the block slide?
e. 3. A ball of mass .075 kg is loaded onto a spring with a spring constant of 500 N/m. The spring is compressed 3.5 cm from equilibrium and is located at the top of a ramp that is 1.4 m high. The ball is then release so that the spring will shoot the ball down the slope. How fast is the ball moving when it is half-way down the slope?
f. 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
g. 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 K 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.)
h. 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
i. the rabbit is 1.7 kg, and the coefficient of kinetic friction a, for ice is .15. If the rabbit is initially
j. 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.)