Biomechanics Practice Problems

The coefficient of static friction between a sled and the snow is 0.19, with a coefficient of dynamic friction of 0.16. A 25 kg girl sits on her sled facing down a 10-degree hill. What is the minimum push her friend needs to exert to start moving down the hill? After getting a push, does she continue to slide down the hill? Explain.

(>4 N push downhill to start moving; yes, she continues to slide after a push; Fdownhill = 43 N; Fstatic friction uphill = 47 N; Fdynamic friction uphill = 39 N)

Two people are playing tug-of-war. Due to their choice of footwear, their coefficient of static friction is different. Participant 1 has a mass of 60 kg, a coefficient of static friction of 2.0, and can pull with a maximum force of 1000 N. Participant 2 has a mass of 80 kg and a coefficient of static friction of 1.2, and can pull with a maximum force of 1200 N. Who wins?

(participant 1 wins)

A track athlete running at fast pace had an instantaneous resultant force of 2800 N acting through the heel during heel strike. If the angle of the resultant force was 120 degrees with respect to the horizontal, what were the horizontal and vertical forces acting on the heel? Estimate his body mass if you know that in general vertical ground reaction force found in running are about 4.3 times the value of body weight.

-1400 N horizontal; 2425 N vertical; 56-kg

A football player pushes a 400 kg tackling sled with a force of 800 N. If the resulting acceleration of the sled is 1.5 m/s/s, what is the magnitude of the friction force opposing the motion of the sled?

-200 N

A 90-kg ice hockey player collides head-on with an 80-kg ice hockey player. If the first person exerts a force of 450 N on the second player, how much force does the second player exert on the first?

-450 N

An 85 kg cyclist (person + bike) was traveling at a constant speed level road. Upon starting up a hill with a 15-degree inclination, the cyclist stopped pedaling and coasted. What was the total downhill force acting on the cyclist considering the coefficient of friction between the tires and the road is 0.1?

138 N downhill

How much force must be applied by a kicker to give a stationary 2.5-kg ball an acceleration of 40m/s/s?

100 N

A soccer ball is kicked from the playing field at a 45˚ angle. If the ball is in the air for 3 seconds, what is the maximum height achieved?

11.25m

A 70-kg skier is in a tuck position and moving down a 20-degree hill. Air resistance applies a resultant force of 15 N against the movement of the skier. The coefficient of friction between the skis and the snow is 0.09. What is the resultant downhill force acting on the skier?

165 N downhill

A high jumper with a body weight of 712 N exerts a force of 3000 N against the ground during takeoff. How much force does the ground on the high jumper exert?

3000 N

If a 70 kg person was sitting on a swing (centered evenly in the middle between the two ropes), what was the force being supported by each rope (in Newtons)? If the same person was sitting in the middle of a hammock, and each rope had an angle of 30 degrees with respect to the horizontal, how much force was each rope supporting? (Note: Force in the rope is not the same in the two situations.)

350 N each; 700 N each

A mountain biker encounters a deep gorge. He has "heard" that if he jumps off the log on the edge of his side of the gorge he can expect 50° for his trajectory. He has also "heard" that the other side of the gorge is 1 meters higher that the side he is on. He knows that he can ride to a maximum speed of 20 mi/hr on the trail approaching the gorge and off of log. Assuming what the rider "heard" is accurate, how wide can the gorge be for him to not plummet to his death?

6.9m

A 65-kg runner had a maximal vertical ground reaction force of 1700 N while running at moderate pace. What was the runner's weight in Newtons? What is the maximal vertical ground reaction force when expressed in multiples of body weight (1 body weight is the weight of the runner).

650 N; 2.62 times greater than body weight

The coefficient of friction between a basketball shoe and a court is 0.56, and the normal reaction force acting on the shoe is 350 N. How much horizontal force is required to make the shoe slide?

>196 N

A rugby player attempts a kick after scoring a try. The ball was kicked at an angle of 60 degrees with an initial resultant velocity of 40 miles/hour! a. What was the initial resultant velocity in meters/second? b. What was the initial horizontal velocity in m/s? c. What was the initial vertical velocity in m/s? d. If the player was 40 meters away from the goal, and the height of the horizontal bar was 3 meters, did the player score? Assume that the trajectory of the ball was on target!

a. 17.9m/s b. 9m/s c. 15.5m/s d. No

A soccer ball is kicked with an initial horizontal speed of 5 m/s and an initial vertical speed of 3 m/s. Assuming projection and landing heights are the same, identify the following quantities: a. The ball's horizontal speed 0.5 seconds into its flight b. The balls horizontal speed midway through its flight c. The balls horizontal speed immediately before contact with the ground d. The ball's vertical speed at the apex of flight e. The ball's vertical speed midway through its flight f. The ball's vertical speed immediately before contact with the ground

a. 5m/s b. 5m/s c. 5m/s d. 0m/s e. 0m/s f. 3m/s

The world record for the 24-hour run is about 160 miles. What is this distance in meters? What is 24 hours in seconds? What would be a runner's average speed in going 160 miles in a day?

answer: 2.98 m/s

1. An orienteer runs north at 5 m/s for 120 seconds, and then west at 4 m/s for 180 seconds. What is the resultant displacement with respect to the starting position? Provide an angle with respect to the north direction.

answer: 937.2 m; 50.2 degrees

A skier was gliding downhill at 15 m/s. How long did it take her to ski the 630 m to the base of the hill ? A less proficient skier averaged 12 m/s down the slope. If they started together, how far behind the first skier was he by the time she got to the bottom of the hill ? (describe this in both time and distance.)

answers: 10.5 s; 126 m

The table below shows the instantaneous velocity of a different bobsled during the first 10 seconds after the driver and crew had gotten on board. Plot a velocity vs Time graph from the data and answer the following questions: What was the sled's acceleration in the first 5 seconds? How far did the sled travel during those 5 seconds? What was the sled's average velocity during the first 5 seconds? Finally, describe what was happening to the bobsled's motion after 8 seconds.

answers: 3.5 m/s/s; 73.75 m; 14.75 m/s

Bobsleds accelerate from rest to high speeds in a few seconds. If one sled's speed increased from 0 to 32 m/s in 8 seconds, what was its average acceleration during that time period? How far did the sled travel down the track in the 8 seconds?

answers: 4 m/s/s; 128 m