This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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You're on a roll — Here are the solutions to the problems: 7. A garden roller with a mass of 200 kg is pushed by a man at a constant speed over a lawn by exerting a constant force of 400 N on the handle of the roller that forms an angle of 60° to the horizontal. Given: Mass of the roller, m = 200 kg Applied force, F = 400 N Angle below the horizontal, = 60° Acceleration due to gravity, g = 9.8 m/s^2 7.1 Calculate the force that causes the roller to move forward. This is the horizontal component of the applied force. Step 1: Calculate the horizontal component (F_x). F_x = F F_x = 400 N × (60°) F_x = 400 N × 0.5 F_x = 200 N The force that causes the roller to move forward is 200 N. 7.2 Calculate the force that tends to pin the roller to the ground. This is the vertical component of the applied force, directed downwards. Step 1: Calculate the vertical component (F_y). F_y = F F_y = 400 N × (60°) F_y = 400 N × sqrt(3)2 F_y ≈ 400 N × 0.8660 F_y ≈ 346.41 N The force that tends to pin the roller to the ground is 346.41 N. 7.3 Calculate the weight (F_g) of the roller. Step 1: Calculate the weight using the formula F_g = m × g. F_g = m × g F_g = 200 kg × 9.8 m/s^2 F_g = 1960 N The weight of the roller is 1960 N. 7.4 Calculate the force that is exerted by the roller on the lawn, i.e., the effective weight of the roller when it is being pushed. The effective weight is the sum of the roller's actual weight and the downward vertical component of the applied force. Step 1: Add the weight and the vertical component. Effective weight = F_g + F_y Effective weight = 1960 N + 346.41 N Effective weight = 2306.41 N The effective weight of the roller when it is being pushed is 2306.41 N.