Answer:
A= 148.92 m/s²
Explanation:
Given that
U(x,y) = (6.00 )x² - (3.75 )y ³
m= 0.04 kg
Now force in the x-direction
Fx= - dU/dx
U(x,y) = (6.00 )x² - (3.75 )y ³
dU/dx= 12 x
When x=0.4 m
dU/dx= 12 x 0.4 = 4.8
So we can say that
Fx= - 4.8 N
From Newtons law
F= m a
- 4.8 = 0.04 x a
a = -120 m/s²
Acceleration in x direction ,a = -120 m/s²
In y -direction
F= - dU/dy
U(x,y) = (6.00 )x² - (3.75 )y ³
dU/dy = 0 - 3.75 x 3 y²
When y = 0.56 m
dU/dy = - 3.75 x 3 x 0.56 x 0.56
dU/dy = - 3.52
So we can say that force in y -direction
F= 3.52 N
F= m a'
3.52 = 0.04 x a'
a'=88.2 m/s²
acceleration in y direction is 88.2 m/s²
The resultant acceleration
A= 148.92 m/s²
Answer:
+2m/s
Explanation:
average velocity = displacement traveled / total time taken
= +12m/ 6s
= +2 m/s
See this suggested solution.
1. Let a force F' is the vector sum of the forces P and Q, then it is shown on the attached picture and marked with red color.
2. according to the condition the force F holds the object, then F should have the same length as the force F' and the opposite direction.
3. using the conditions described in 2. the answer is C.
Answer:
17. h = l − l cos θ
18. 1.40 m
Explanation:
Let's call d the height of the triangle. We can then say:
h = l − d
Using trig, we can write d in terms of l and θ:
d = l cos θ
h = l − l cos θ
If l = 6 m and l cos θ = 40°:
h = 6 − 6 cos 40
h ≈ 1.40
1.15 m/s to the left (3 sig. fig.).
<h3>Explanation</h3>
Momentum is conserved between the two balls if they are not in contact with any other object. In other words,
, where
stands for mass and
stands for velocity, which can take negative values.
Let the velocity of objects moving to the right be positive.
,
.
Before the two balls collide:
,
.
After the two balls collide:
needs to be found, 
.
Again,
,
.
.
is negative? Don't panic. Recall that velocities to the right is considered positive. Accordingly, negative velocities are directed to the left.
Hence, ball A will be travelling to the left at 1.15 m/s (3 sig. fig. as in the question) after the collision.
