Help on these few questions please? :( I'm so confused. No need for a direct answer if you don't wanna give it but I just need some explaining. thank you.
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A ball is thrown horizontally from a platform so that the initial height of the ball is 6.0 m above the level ground below. The ball lands 24 m from its original horizontal location. Find how fast the ball was thrown. Show all work.
A car is driven at constant velocity along a level highway. Indicate the value of the net force and list all the main forces acting on the car to produce the net force. Clearly explain what produces or exerts each of the contact forces acting on the car and explain which forces are balanced.
Summarize two observations that are contrary to the predictions based on Newton’s laws but that confirm Einstein’s explanation of gravity. Indicate how the predictions based on Newton’s theory differ from Einstein’s.
1. h = 0.5g*t^2 = 6 m.
4.9t^2 = 6
t^2 = 1.224
Tf = 1.107 s. = Fall time.
d = Xo * Tf = 24 m.
Xo * 1.107 = 24
Xo = 21.7 m/s = Initial velocity.
2. Fg = m*g = Force of gravity = Wt. of
car.
Fk = u*Fg = Force of kinetic friction.
Fn = Fap-Fk = Net force.
Fap = Force applied.
Sure, I'd be happy to help explain these questions to you! Let's break them down one by one:
1. A ball is thrown horizontally from a platform with an initial height of 6.0 m above the ground. The ball lands 24 m from its original location. We need to find the initial speed (also known as the initial velocity) of the ball.
To solve this problem, we can use the kinematic equation for horizontal motion:
distance = velocity × time
In this case, the ball is thrown horizontally, which means its initial vertical velocity is 0 m/s. Therefore, the only factor that affects the horizontal distance traveled is the initial horizontal velocity.
Given that the ball lands 24 m away and neglecting air resistance, we can assume the time of flight is the same as the time it would take to drop vertically from the initial height of 6.0 m to the ground. We can use the kinematic equation for vertical motion to find the time of flight:
distance = 1/2 × acceleration × time^2
Since the ball is dropping vertically, the acceleration is due to gravity (approximately 9.8 m/s^2).
By substituting the values into the equation, we get:
6 = 1/2 × 9.8 × time^2
Now we can solve for time:
time^2 = 6 / (1/2 × 9.8) = 1.22
time = √(1.22) = 1.1 s (approximately)
Finally, we can find the initial horizontal velocity using the distance formula:
distance = velocity × time
24 = velocity × 1.1
velocity = 24 / 1.1 = 21.8 m/s (approximately)
Therefore, the ball was thrown with an initial velocity of approximately 21.8 m/s.
2. A car is driven at a constant velocity along a level highway, and we need to determine the net force acting on the car and list all the main forces involved.
When an object is moving at a constant velocity, the net force acting on it is zero. This means that all the forces acting on the object must be balanced. In the case of the car, the main forces acting on it are:
- The force of friction: This force arises from the interaction between the car's tires and the road surface. It opposes the motion of the car and is what allows the car to accelerate, decelerate, or maintain a constant velocity. The frictional force is exerted by the road surface on the tires.
- The force of gravity: This force is the weight of the car, which is the product of its mass and the acceleration due to gravity (approximately 9.8 m/s^2). The force of gravity is exerted by the Earth on the car, pulling it downward.
- The normal force: This force is the support force exerted by the road surface on the car, perpendicular to the surface. It acts to balance the vertical component of the force of gravity, preventing the car from sinking into the road or lifting off.
Since the car is moving at a constant velocity, the net force is zero. This means that the force of friction must be equal in magnitude and opposite in direction to the force of gravity. The normal force also balances the vertical component of the force of gravity.
3. This question asks for two observations that are contrary to the predictions based on Newton's laws but support Einstein's explanation of gravity, as well as the differences between Newton's and Einstein's theories.
One observation that contradicts Newton's predictions is the phenomenon of gravitational time dilation. According to Newton's laws of motion, time should flow uniformly everywhere in the universe, regardless of the strength of the gravitational field. However, Einstein's theory of general relativity predicts that time actually flows slower in regions of stronger gravitational fields. This prediction has been confirmed by experiments, such as the Hafele-Keating experiment, where atomic clocks on airplanes were found to tick slightly slower relative to synchronized clocks on the ground.
Another observation that supports Einstein's explanation of gravity is the bending of light around massive objects. According to Newton's theory, light should travel in straight lines. However, Einstein's theory predicts that the gravitational field of a massive object, such as a star or a black hole, can bend the path of light. This prediction was confirmed during the 1919 Solar Eclipse expedition, where the bending of starlight passing close to the Sun was observed, validating Einstein's theory of general relativity.
The main differences between Newton's theory of gravity and Einstein's theory of general relativity are as follows:
- Newton's theory describes gravity as a force acting instantaneously at a distance between massive objects, without providing a mechanism for its propagation. On the other hand, Einstein's theory explains gravity as the curvature of spacetime caused by massive objects, where objects move along geodesics in this curved spacetime.
- Newton's theory assumes that time flows uniformly everywhere, whereas Einstein's theory predicts that time is influenced by the presence of mass and gravity, resulting in phenomena like gravitational time dilation.
- Newton's theory does not explain the observed bending of light, while Einstein's theory accurately predicts this effect by accounting for the curvature of spacetime caused by massive objects.
I hope these explanations help clarify the concepts for you! Let me know if you have any further questions.