A box with an initial speed of #7 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #5/6 # and an incline of #pi /4 #. How far along the ramp will the box go?
The distance is
Consequently, the object's net force is
Newton's Second Law states
A deceleration is indicated by the negative sign.
We utilize the equation of motion.
By signing up, you agree to our Terms of Service and Privacy Policy
To find the distance along the ramp the box will go, you can use the following steps:
- Calculate the acceleration of the box along the ramp due to gravity.
- Calculate the frictional force acting against the motion of the box.
- Calculate the net force acting on the box along the ramp.
- Use the net force to find the acceleration of the box along the ramp.
- Use the kinematic equation to find the distance along the ramp the box will go.
Let's start by finding the acceleration of the box along the ramp due to gravity:
Acceleration due to gravity along the ramp = g * sin(π/4)
Next, calculate the frictional force acting against the motion of the box:
Frictional force = coefficient of kinetic friction * normal force
Normal force = weight of the box * cos(π/4)
Now, calculate the net force acting on the box along the ramp:
Net force = gravitational force along the ramp - frictional force
Use the net force to find the acceleration of the box along the ramp:
Acceleration along the ramp = Net force / mass of the box
Finally, use the kinematic equation to find the distance along the ramp the box will go:
Distance along the ramp = (initial velocity * time) + (0.5 * acceleration along the ramp * time^2)
where time can be found using the equation: time = final velocity / acceleration along the ramp, and the final velocity is 0 m/s since the box comes to rest.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- A #30# #kg# object on Venus weighs #266.1# #N#. What is the value of {the acceleration due to} gravity on Venus?
- An object with a mass of # 3 kg# is lying still on a surface and is compressing a horizontal spring by #60 c m#. If the spring's constant is # 6 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?
- If the length of a #24 cm# spring increases to #92 cm# when a #5 kg# weight is hanging from it, what is the spring's constant?
- An object with a mass of #4 kg# is hanging from a spring with a constant of #3 (kg)/s^2#. If the spring is stretched by # 12 m#, what is the net force on the object?
- Why is inertia not a force?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7