1. A snowmobile, with a mass of 530 kg, applied a force of 410 N backwards on the snow.
a. What force is responsible for the snowmobile’s resulting forward motion? (Hint: Think action–reaction force pairs.)
b. If the force of friction on the snowmobile is 187 N backwards, what is the net force acting on the snowmobile?
c. What is the acceleration of the snowmobile?
d. If the snowmobile accelerates for 7.3 s, what is its final speed?
e. How far would the snowmobile travel in this time?
f.The image above shows a person being “thrown” backwards as the snowmobile accelerates underneath him. Why would this happen?
a. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this case, when the snowmobile applies a force of 410 N backwards on the snow, the snow exerts an equal and opposite force of 410 N forwards on the snowmobile. Therefore, the force responsible for the snowmobile's resulting forward motion is also 410 N.
b. To find the net force, you need to subtract the force of friction from the force responsible for forward motion. In this case, the force of friction is 187 N backwards. So, the net force acting on the snowmobile would be the force responsible for forward motion (410 N) minus the force of friction (187 N), giving a net force of 223 N.
c. To find the acceleration, you can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula is written as F = ma, where F is the net force, m is the mass, and a is the acceleration. Rearranging the formula to solve for acceleration, we have a = F/m. Plugging in the values, the acceleration of the snowmobile would be 223 N / 530 kg, which is approximately 0.42 m/s².
d. To find the final speed of the snowmobile, you can use the equation v = u + at, where v is the final velocity, u is the initial velocity (assumed to be 0, as the problem does not provide the initial speed), a is the acceleration, and t is the time. Since the snowmobile accelerates for 7.3 s and the initial velocity is 0, the equation simplifies to v = at. Plugging in the values, the final speed of the snowmobile would be 0.42 m/s² * 7.3 s, giving a final speed of approximately 3.07 m/s.
e. To find the distance traveled, you can use the equation s = ut + 0.5at², where s is the distance traveled, u is the initial velocity (0 as in the previous question), a is the acceleration, and t is the time. Since the initial velocity is 0, the equation simplifies to s = 0.5at². Plugging in the values, the distance traveled by the snowmobile would be 0.5 * 0.42 m/s² * (7.3 s)², giving a distance of approximately 1.31 meters.
f. The person being thrown backwards is an example of Newton's third law of motion. According to the law, if the snowmobile exerts a force on the person, pushing them backwards, the person will exert an equal and opposite force on the snowmobile, causing it to move forward. This is because every action has an equal and opposite reaction. So, as the snowmobile accelerates forward, the person experiences a backward force, resulting in their apparent "throw" or displacement backwards.