How Far Does a Block Travel Up an Incline Before Stopping?

AI Thread Summary
A block with an initial velocity of 3 m/s travels up a 30-degree incline before stopping, with a friction coefficient of 0.5. The forces acting on the block include gravitational force and friction, leading to the equation mgsin(30) - (0.5)*mgcos(30) = ma. The mass cancels out, allowing for the calculation of acceleration, which was initially found to be positive. However, the calculation of the gravitational force was identified as incorrect, indicating a need for reevaluation. The discussion focuses on resolving the error in the force calculations to determine the correct distance traveled up the incline.
PhizKid
Messages
477
Reaction score
2

Homework Statement


A block of unknown mass is sent up an incline plane of 30 degrees with an initial velocity of 3 m/s. The coefficient of friction is 0.5. Find the distance the block travels up the incline before it stops.


Homework Equations


F = ma
v^2 = (v_0)^2 + 2a(x - x_0)


The Attempt at a Solution


So the vertical forces of the incline are the normal force which is equal to mgcos(30). Therefore, the force of friction is (0.5)*mgcos(30).

So taking going up the incline to be positive, we have mgsin(30) - (0.5)*mgcos(30) = ma. We can cancel out the masses. So then we have acceleration = ((2-sqrt(3))(9.8)/4. This turns out to be positive, but it should be negative because the friction should overcome gravity eventually (maybe not, but this problem is implying it). What did I do wrong so far?
 
Physics news on Phys.org
Never mind, I calculated the horizontal force of gravity incorrectly
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Spring and block on an inclined plane
Replies
27
Views
9K
Block on top of an inclined plane, with a rough surface, that moves with constant acceleration
Replies
41
Views
4K
Inclined Plane Static Friction Coefficient
Replies
11
Views
4K
How Does Friction Affect Acceleration on an Incline?
Replies
19
Views
3K
Block on an incline and frictional force
Replies
9
Views
13K
Box and a Spring on on an inclined plane
Replies
11
Views
3K
What is the coefficient of friction in this inclined plane problem?
Replies
2
Views
1K
Acceleration on an inclined plane
Replies
3
Views
2K
Dynamics problem involving an inclined plane and Friction
Replies
1
Views
2K
Help with finding Normal Force of inclined plane
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top