Here are some problems that I have figured out. Am I doing them right? 47.) A trapeze artist weighs 800N. The artist is momentarily held to one sid of a swing by a partner so that both of the swing ropes are at an angle of 30.0 degrees with the vertical. In such a condition of static equilibrium, what is the horizontal force being applied by the partner? tan30 = opp/800. F = 800tan30 = 462N. Is this right? 65.) A 40.0N crate is pulled uip a 5.0m inclined plane at a constant velocity. If the plane is inclined at an angle of 37 degrees to the horizontal and there is a constant force of friction of 10.0 N between the crate and the surface, what is the net gain in potential energy by the crate? Potential Energy = mgh. (40*5)-(40*0) = 200 J. However, the choices for this question are 120J, -120J, 210J, -210J. What am I doing wrong here? 68.) A child riding a bicycle has a total mass of 40.0kg. The child approaches the top of the hill that is 10.0m high and 100.0m long at 5.0 m/s. If the force of friction between the bicycle and the hill is 20.0N, what is the child's velocity at the bottom of the hill? Force of gravity causes a force of 392.4N, 392.4cos84.26 = the applied force results in 39.25N. Net force = 19.25N, which gives a final velocity of 11 m/s. Is this correct? 85.) To warm up before a game, a baseball pitcher tosses a 0.15kg ball by rotating his forearm, which is 0.32m in length, to accelerate the ball. The ball starts at rest and is thrown at a speed of 12 m/'s in 0.40s. While the ball is in the pitcher's hand, what torque is applied to the ball to produce the angular acceleration? I calculated that the acceleration created from his arm = 30 rad/sec^2. Torque = moment of inertia * ang. acceleration. Im missing my other paper of notes but my final calculations yield an answer of 1.4 N-m. Is this correct? 96.) A grinding wheel with a moment of inertia of 2.0kg-m^2 is initially at rest. What angular momentum will the wheel have 10.0 s after a 2.5 N-m torque is applied to it? I calculated angular acceleration to = 1.25 rad/sec^2. Multiplied by 10 secs, that gives an angular speed of 12.5 rad/sec. Multiplied by the moment of inertia gives 25 kg-m/s^2 of Angular momentum. Is this correct? 100.) A bucket filled with water has a mass of 23kg and is attached to a rope that is woundwith a crank arounda 0.05m radius cylinder at the top of a well. The moment of inertia of the cylinder and crank is 0.12kg-m^2. The bucket and water are first raised to the top of the well and then released to fall back into the well. What is the rotational kinetic energy of the cylinder and crank at the instant the bucket is moving at a speed of 7.9 m/s? I calculated that it took .81 s for the bucket to fall to a speed of 7.9 m/s. I calculated that the angular speed was 81.65 rad/sec. KE = (1/2)Iw^2 = (1/2)(.12)(81.65^2) = 400 Joules. Is this correct?