Final answer:
The horizontal acceleration of the sled is -0.053 m/s², and the force needed to pull the sled at a constant velocity is 29.4 N.
Step-by-step explanation:
Given a 15-kg sled is pulled across a horizontal, snow-covered surface by a force applied to a rope at 30 degrees with the horizontal and a coefficient of kinetic friction between the sled and the snow of 0.20, we can solve for the horizontal acceleration of the sled and the force needed to pull the sled at a constant velocity.
(a) To find the horizontal acceleration, we need to determine the net force acting on the sled. The net force is equal to the applied force minus the force of friction. Since the force applied is at an angle of 30 degrees with the horizontal, we need to find its horizontal component. The horizontal component of the applied force is calculated by multiplying the applied force by the cosine of the angle: Fx = 33 N * cos(30°) = 28.6 N. The force of friction can be determined using the equation: force of friction = coefficient of kinetic friction * normal force. The normal force is equal to the weight of the sled, which is given by the formula: weight = mass * acceleration due to gravity. Plugging in the values, we get: normal force = 15 kg * 9.8 m/s² = 147 N. Therefore, the force of friction = 0.20 * 147 N = 29.4 N. The net force can now be calculated: net force = Fx - force of friction = 28.6 N - 29.4 N = -0.8 N. Since the sled is being pulled to the right and the net force is negative, the acceleration is also negative. Therefore, the horizontal acceleration of the sled is -0.8 N / 15 kg = -0.053 m/s².
(b) To find the force needed to pull the sled at a constant velocity, we need to determine the force of friction. If the sled is moving at a constant velocity, the net force is zero. Therefore, the force of friction must be equal in magnitude but opposite in direction to the applied force. Using the same formula as before, we can calculate the force of friction: force of friction = coefficient of kinetic friction * normal force = 0.20 * 147 N = 29.4 N. Therefore, the force needed to pull the sled at a constant velocity is 29.4 N.