1. Two 20.-newton forces act concurrently on an object. What angle between these forces will produce a resultant force with the greatest magnitude?
(1) 0°
(2) 45°
(3) 90.°
(4) 180.°
2. A rock is thrown straight up into the air. At the highest point of the rock’s path, the magnitude of the net force acting on the rock is
(1) less than the magnitude of the rock’s weight, but greater than zero
(2) greater than the magnitude of the rock’s weight
(3) the same as the magnitude of the rock’s weight
(4) zero
And can you please explain why? Thanks.
1. F max = 20 + 20 = 40 N. @ 0o.
2. The velocity is zero and not
changing; therefore, the acceleration is zero also. F = M*a = M*0 = 0.
1. The angle between the two forces that will produce the greatest magnitude of the resultant force is 180°, option (4). This is because when two forces act in opposite directions and are aligned with each other (180° apart), they will cancel each other out completely and create the largest magnitude of the resultant force. It's like when you try to hug someone, but they want nothing to do with hugs, so they move away completely. Maximum rejection, maximum resultant force!
2. At the highest point of the rock's path, the magnitude of the net force acting on the rock is zero, option (4). This is because at the highest point, the rock momentarily comes to a stop before reversing direction and falling back down. When the rock reaches this point, the upward force provided by the throw is equal and opposite to the force of gravity pulling it down, resulting in a net force of zero. It's like when you're on a roller coaster and you reach the top of the hill, that brief moment of weightlessness when you feel like you're floating. So at the highest point, the net force is having a vacation, taking a break from all the hard work!
1. To find the angle between two forces that will produce a resultant force with the greatest magnitude, we need to use vector addition. The magnitude of the resultant force is given by the equation:
R = √(F₁² + F₂² + 2F₁F₂cosθ)
where R is the resultant force, F₁ and F₂ are the magnitudes of the individual forces, and θ is the angle between them.
To maximize the magnitude of the resultant force, we want to maximize the term 2F₁F₂cosθ. The value of cosθ is maximum when θ = 0° (cos 0° = 1), so the angle that will produce the resultant force with the greatest magnitude is 0°. Therefore, the correct answer is (1) 0°.
2. At the highest point of the rock's path, the magnitude of the net force acting on the rock is zero. This is because the rock momentarily comes to a stop at the highest point of its trajectory before falling back down due to the force of gravity.
At that point, the gravitational force pulling the rock downwards is exactly balanced by an equal but opposite force exerted by the rock in the upward direction (which we call the net force). This balancing of forces results in the net force being zero.
Therefore, the correct answer is (4) zero.