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.
ScanSolve AI Answer
15. a) ii) The weight of the body on the planet Step 1: Identify the given values and the formula. Mass of the body m = 50 \, g = 0.050 \, kg. Acceleration of gravity on the planet g = 1.66007 \, m/s^2 (calculated in part i)). The formula for weight is W = mg. Step 2: Substitute the values into the formula and calculate the weight. W = (0.050 \, kg)(1.66007 \, m/s^2) W = 0.0830035 \, N Rounding to two significant figures: W ≈ 0.083 \, N The weight of the body on the planet is 0.083 N. b) Explain this observation. When the cardboard is pulled away suddenly, the coin remains in its original state of rest due to its inertia. The frictional force between the coin and the cardboard is insufficient to accelerate the coin horizontally with the cardboard. As the cardboard moves out from under it, the coin falls into the can due to gravity. c) A man of mass 80 \, kg is standing in a lift. What force does he exert in the floor when the lift is We will use g = 9.8 \, m/s^2 for the acceleration due to gravity on Earth. The force exerted by the man on the floor is equal to the normal force N exerted by the floor on the man. i) At rest. Step 1: Identify the given values. Mass m = 80 \, kg. Acceleration a = 0 \, m/s^2 (at rest). Acceleration due to gravity g = 9.8 \, m/s^2. Step 2: Apply Newton's second law. Since the lift is at rest, the net force is zero. The normal force N balances the man's weight mg. N - mg = ma N - mg = m(0) N = mg Step 3: Calculate the force. N = (80 \, kg)(9.8 \, m/s^2) N = 784 \, N The force exerted on the floor is 784 N. ii) Accelerating upwards at 4 \, m/s^2. Step 1: Identify the given values. Mass m = 80 \, kg. Acceleration a = 4 \, m/s^2 (upwards). Acceleration due to gravity g = 9.8 \, m/s^2. Step 2: Apply Newton's second law. When accelerating upwards, the net force is upwards. N - mg = ma N = mg + ma N = m(g+a) Step 3: Calculate the force. N = (80 \, kg)(9.8 \, m/s^2 + 4 \, m/s^2) N = (80 \, kg)(13.8 \, m/s^2) N = 1104 \, N The force exerted on the floor is 1104 N. iii) Moving downwards at an acceleration 3 \, m/s^2. Step 1: Identify the given values. Mass m = 80 \, kg. Acceleration a = 3 \, m/s^2 (downwards). Acceleration due to gravity g = 9.8 \, m/s^2. Step 2: Apply Newton's second law. When accelerating downwards, the net force is downwards. mg - N = ma N = mg - ma N = m(g-a) Step 3: Calculate the force. N = (80 \, kg)(9.8 \, m/s^2 - 3 \, m/s^2) N = (80 \, kg)(6.8 \, m/s^2) N = 544 \, N The force exerted on the floor is 544 N. That's 2 down. 3 left today — send the next one.