Question

1. Imagine that you’re sledding alone down a steep hill on a toboggan and that you left the top of the hill at the same time as an identical toboggan, loaded with 4 people.

a. Which toboggan will reach the bottom of the hill first?

b. If you took a toboggan down a 2% grade slope, for a 1000 foot run, and then you took the toboggan down a steeper route of 15% grade down the hill, how would that affect the speed of your descent? Explain.

c. Before each downhill run, you must pull the toboggan back to the top of the hill. If the Hill is 1000 vertical feet, how many runs will you do in 2 hours?

d. Why can you sled down a hill? But you can’t you skate down a hill?

e. How do snow shoes help you walk in snow? Why are their different sized snow shoes?

2. a. Why is hip movement and turning the knees important in improving a golf swing?

b. During the back swing, are you accelerating?

c. At the moment you reach the bottom of the swing you make contact with the ball. Explain how energy is transferred from the club to the ball

d. Why is there more stress on a golfers shoulders at the start of the swing, than when hitting the ball?

e. Why do you need to follow through on the swing?

f. What has happened when a golf shot is hooked?

g. What is the sweet spot on a club and what does it do?

h. What is a ping sound and how is it produced when hitting a golf ball?

Answer 1

SOLUTION

Problem 1

Part (a)

The free body diagram of each sled is shown below:

Now applying the second Newton's Law for the fisrt sled we have:

But,

Inserting (2) into (1) we obtain:

Similarly, for the second Sled we have:

Because both sleds descend with the same acceleration then both sleds arrive at the foot of the hill at the same time.

Part (b)

For

Replacing (5) into equation (4) we have:

Now, the speed at the bottom of the hill can be obtained using:

Replacing (6) and 1000 feet=304.8 m into equation (7) we have:

Solving we obtain:

Similarly, for we have :

Inserting (9) into (7) we have:

Solving we obtain:

Comparing (8) with (10) we can affirm that as the slope of the hill increases in value then the sledge increases in speed.

Part (c)

Assuming an angle of 15 degrees, the time to descend can be calculated using:

Inserting data given values:

solving we obtain:

Now, the time to climb depends on the force applied on the sled. Assuming a time to go up of 10 min we can say that in 2 hours the sled makes 11-12 runs.

Part (d)

This is because the contact area between the skid and the ground is smaller than in the case of the sled. For this reason, in winter games, skaters descending a hill use skates from a much larger area than the skates used during a horizontal movement.

Part (e)

Snowshoes work by having a larger area than the bottom of the boot or tennis shoe. That larger surface area means you have more snow supporting the weight of your body from below when you use a snowshoe than you would if you were wearing conventional shoes. That additional surface also redistributes the weight that descends on the snow from above. The pressure exerted depends on the surface area, the snowshoes have a greater surface and therefore the pressure is lower which implies that the weight supported is lower.