Question

A van accelerates down a hill (see figure below), going from rest to 30.0 m/s in 5.30 s. During the acceleration, a toy (m = 0.210 kg) hangs by a string from the van's ceiling. The acceleration is such that the string remains perpendicular to the ceiling.

a) Determine the angle

b) Determine the tension in the string

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Answer 1

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Answer 2

35.239 degrees

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Answer 3

mgsin(theta)=ma

theta=arcsin(a/g)

a=(v2-v1)/time

tension=mgcos(theta)

Answer 4

  Here is what I solved before. Please substitute the figures as per your question. Let me know if you want some clarification on it. Please rate 5 stars if I succeeded in helping you.

A van accelerates down a hill, going from rest to 30m/s in 6.00s. During acceleration, a toy (m=0.100kg) hangs by a string from the van's ceiling. The acceleration is such that the string remains perpendicular to the ceiling. Determine a) the angle ? and b) the tension in the string.   

                                            
mg

   from the free body diagram the accelerationcomponents of the toy will be

   a_y = 0

   ax = ? v_x / ?t

        = 30.0 m/s / 6.00s

        =...... m/s²

(a)

   to find the angle we apply the newtonssecond law of motion to the toy which gives

   ?F_x = m g sin?

          = ma_x

   so the angle will be

   ? = sin^-1(a_x /g)   

      = ......^o

(b)

   ?F_y = T - m g cos?

          = ma_y

          =0

   the tension will be

   T = m g cos?

       = ....... N   

Answer 5

The average velocity Vavg = 30.0m/s / 2 = 15 m/s

so the distance covered was s = Vavg * t = 15.0m/s * 5.30s = 79.5 m

and s = 79.5 m =

Answer 6

tension = 1.6825 N

Answer 7

v = u +a*t

30 = 0 +a*5.3

a= 5.66 m/s^2

g*sin(theta) = 5.66

sin(theta) = 5.66/9.81

a) theta = 35.24 degree

b)

T = mg*cos(theta)

= 0.21*9.81*cos(35.24) = 1.682 N

Answer 8

Answer 9

The average velocity Vavg = 30.0m/s / 2 = 15 m/s

so the distance covered was s = Vavg * t = 15.0m/s * 5.30s = 79.5 m

and s = 79.5 m =

Answer 10

1)mgsin(theta)=ma

mgcos(theta)=T

a=(30/5.3)

a=5.67m/s^2

sin(theta)=5.67/9.8

theta=35.28

2)T=mgcos(theta)=0.8*9.8*0.21

T=1.68N