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Canadian

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Just got the midterm back, I got 80% (not too bad considering the class average was 55%).

Anyway there were two questions that I got completely wrong, not even a partial mark.

First Question: Part A:Consider a lawnmower of weight W which can slide across a horizontal surface with a coefficient of friction (mu) . In this problem the lawnmower is pushed using a massless handle, which makes an angle theta with the horizontal. Assume that , the force exerted by the handle, is parallel to the handle. Take the positive x direction to be to the right and the postive y direction to be upward. Find the magnitude of the force required to slide the lawnmower over the ground at constant speed by pushing the handle. Express the required force in terms of given quantities.

Part B:The solution for part a has a singularity (that is, becomes infinitely large) at a certain angle (theta "critical") . For any angle , the expression for F(handle) will be negative. However, a negative applied force F(handle) would reverse the direction of friction acting on the lawnmower, and thus this is not a physically acceptable solution. In fact, the increased normal force at these large angles makes the force of friction too large to move the lawnmower at all. Find an expression for tan(theta critical)

Question 2: Quarterback Fred is going to throw a pass to tight end Doug. Doug is 20 m in front of Fred and running straight away at 6.0 m/s when Fred throws the 500 g football at a 40 angle. Doug catches the ball without having to alter his speed and runs for the game-winning touchdown. How fast did Fred throw the ball?

For question one, I found the horizontal and vertical components of the pushing force set them to 0 and then set them equal to each other then solved for F, I think for this question I am missing something to do with the force of friction and how it is affected by the pushing handle. I didn't get part two.

For question 2 my scrap paper sheet was lost, so I'm not exactly sure what I did but the answer I got (was wrong) was that the speed of the ball was greater than 6 m/s. The marker wrote on the sheet that they were looking for a single numerical value.

Any help would be greatly appreciated, it's not worth anything now I just want to understand what I did wrong and what I should have done to solve the problems.

Thanks