There are NO true statements on the list you provided.
The answer is d! I’m happy to help :)
Yes. It's (speed squared)/(radius of the circle).
Answer:
The unbalanced force that caused the ball to stop was friction
Explanation:
As Newton's second law states, the acceleration of an object is proportional to the net force applied on the object:
therefore, in order to move at constant speed, an object should have a net force of zero (balanced forces) acting on it.
In this case, the ball slows down and eventually comes to a stop: it means that the ball is decelerating, so there are unbalanced forces (net force different from zero) acting on it. The unbalanced force acting on the ball is the friction: friction is a force against the motion of the object, which is due to the contact between the surface of the ball and the surface of the street, and this force is responsible for slowing down the ball.
Either 175 N or 157 N depending upon how the value of 48° was measured from.
You didn't mention if the angle of 48° is from the lug wrench itself, or if it's from the normal to the lug wrench. So I'll solve for both cases and you'll need to select the desired answer.
Since we need a torque of 55 N·m to loosen the nut and our lug wrench is 0.47 m long, that means that we need 55 N·m / 0.47 m = 117 N of usefully applied force in order to loosen the nut. This figure will be used for both possible angles.
Ideally, the force will have a 0° degree difference from the normal and 100% of the force will be usefully applied. Any value greater than 0° will have the exerted force reduced by the cosine of the angle from the normal. Hence the term "cosine loss".
If the angle of 48° is from the normal to the lug wrench, the usefully applied power will be:
U = F*cos(48)
where
U = Useful force
F = Force applied
So solving for F and calculating gives:
U = F*cos(48)
U/cos(48) = F
117 N/0.669130606 = F
174.8537563 N = F
So 175 Newtons of force is required in this situation.
If the 48° is from the lug wrench itself, that means that the force is 90° - 48° = 42° from the normal. So doing the calculation again (this time from where we started plugging in values) we get
U/cos(42) = F
117/0.743144825 = F
157.4390294 = F
Or 157 Newtons is required for this case.
