A block with mass m = 13 kg is projected up a rough incline angled at ? = 30 deg

Question

A block with mass m = 13 kg is projected up a rough incline angled at ? = 30 degrees to the ground with a speed of v = 6.4 m/s. Just after release, a small booster strapped to the block ignites, providing a constant thrust of T = 100 N as the block travels up the incline. The coefficient of friction between the block and ramp is ? = 0.25. If the booster cuts out at d = 5 m up the incline, what is the total distance that the block travels before coming to a stop? Specify your answer in meters to 2 decimal places.

Explanation / Answer

Weight W=Mg=13*9.81= 127.53N

T=100N

=0.25

=30

We will be considering forces in two directions, one parallel to the incline and the other perpendicular to the incline.

Let Normal Reaction from the plane be N

Let friction force be F=N

Considering force balance perpendicular to the plane:

N=WCos= 127.53*0.866=110.44 N

F=N=0.25*110.44=27.611N

Case 1: Before d=5m

Balancing forces parallel to plane:

T-WSin-F=ma

=> ma=8.624N

a=8.624/13=0.66m/s2

Applying kinematics:

v22=v2+2as

=>v22=6.42+2*0.66*5=47.59

v2= 6.898 m/s

Case 2: After d=5m

Balancing forces parallel to plane:

-(WSin+F)=ma

a= -91.376/13 = -7.03m/s2

Applying kinematics:

v32=v22+2as

v3=0 (Since body comes to rest in the end)

6.8982-2*7.03*s=0

=> s= 3.38m

Total distance travelled = Distance in case 1+  Distance in case 2

= 5 + 3.38 = 8.38m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.