A horse is harnessed to a sled having a mass of 231 kg, including supplies. The horse must exert a force exceeding 1250 N at an angle of 36.3° (above the horizontal) in order to get the sled moving. Treat the sled as a point particle.
HINT - Use the relation between the normal force and the maximum static friction force, solving for μs, the coefficient of static friction.
Apply the x-component of Newton's second law with
ax = 0.
(a) Calculate the normal force (in N) on the sled when the magnitude of the applied force is 1250 N. (Enter the magnitude.)
(b)
Find the coefficient of static friction between the sled and the ground beneath it.
(c)
Find the static friction force (in N) when the horse is exerting a force of 6.25 ✕ 102 N on the sled at the same angle. (Enter the magnitude.)
Hey, I did the calculations and got
a - 1258.7 N
b - 1.700 N
c - 3350.739 N
But, the website says the answer is wrong.
wondering how you got so many significant figures out of that. You must believe your calculator
(a) The normal force (N) can be found by resolving the force applied by the horse into its vertical and horizontal components. The vertical component is given by F_vertical = F_applied * sin(theta), where F_applied = 1250 N and theta = 36.3°.
So, F_vertical = 1250 N * sin(36.3°) = 734.62 N.
Therefore, the normal force on the sled is equal to the weight of the sled plus the vertical component of the applied force.
Weight of the sled = mass * gravity = 231 kg * 9.8 m/s^2 = 2263.8 N.
Normal force = Weight of the sled + F_vertical
Normal force = 2263.8 N + 734.62 N = 2998.42 N.
(b) The coefficient of static friction (μs) can be found using the equation μs = F_friction / Normal force.
Since the sled is just about to move, the static friction force (F_friction) is equal to the maximum static friction force. Therefore, μs = F_max_static_friction / Normal force.
F_max_static_friction = μs * Normal force.
By substituting the value of Normal force obtained in part (a) into the equation above, we have:
μs = F_max_static_friction / 2998.42 N.
Unfortunately, we do not have enough information to determine the value of μs because we don't have the maximum static friction force mentioned in the problem.
(c) To find the static friction force when the horse exerts a force of 6.25 * 10^2 N on the sled at the same angle (F_applied), we can use the same method as in part (a).
Vertical component of F_applied = F_applied * sin(theta) = 6.25 * 10^2 N * sin(36.3°) = 368.62 N.
Normal force = Weight of the sled + F_vertical = 2263.8 N + 368.62 N = 2632.42 N.
The static friction force (F_friction) can be found using the equation F_friction = μs * Normal force. However, we still do not have the value of μs, so we cannot calculate the static friction force.
To solve this problem, we need to break it down into individual steps. Let's go through each part of the question and explain how to find the answers.
(a) Calculate the normal force (in N) on the sled when the magnitude of the applied force is 1250 N.
To find the normal force on the sled, we need to understand that the force exerted by the horse at an angle of 36.3° above the horizontal can be resolved into two components: the horizontal component (parallel to the ground) and the vertical component (perpendicular to the ground).
The vertical component of the force is equal to the normal force because the sled is not moving up or down. Therefore, the normal force is equal in magnitude to the force exerted by the horse when it is at an angle.
So, the normal force is 1250 N.
(b) Find the coefficient of static friction between the sled and the ground beneath it.
The coefficient of static friction (μs) relates the maximum static friction force to the normal force. It is given by the equation:
μs = (maximum static friction force) / (normal force)
In this case, we are given the maximum force required to get the sled moving, which is 1250 N. We also found the normal force to be 1250 N. Therefore, the coefficient of static friction can be calculated as:
μs = 1250 N / 1250 N = 1
So, the coefficient of static friction between the sled and the ground is 1.
(c) Find the static friction force (in N) when the horse is exerting a force of 6.25 ✕ 102 N on the sled at the same angle.
To find the static friction force, we need to consider the force exerted by the horse and the coefficient of static friction.
The static friction force is the force applied parallel to the ground to oppose the motion of the sled. It can be calculated using the equation:
static friction force = (coefficient of static friction) * (normal force)
In this case, we are given the coefficient of static friction, which is 1, and the normal force, which we calculated to be 1250 N.
Therefore, the static friction force can be calculated as:
static friction force = 1 * (1250 N) = 1250 N.
So, the static friction force when the horse is exerting a force of 6.25 ✕ 102 N on the sled at the same angle is 1250 N.
my bad
the fraction from (b) is upside down
will change answers (b) and (c)
heed bob on the sig fig
(a) (m * g) - [1250 * cos(36.3º)]
(b) [result from (a)] / [1250 * sin(36.3º)]
(c) [result from (b)] * {(m * g) - [625 * cos(36.3º)]}